196 lines
9.7 KiB
HTML
196 lines
9.7 KiB
HTML
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
|
||
|
|
<html>
|
||
|
|
<!-- This manual is for FFTW
|
||
|
|
(version 3.3.10, 10 December 2020).
|
||
|
|
|
||
|
|
Copyright (C) 2003 Matteo Frigo.
|
||
|
|
|
||
|
|
Copyright (C) 2003 Massachusetts Institute of Technology.
|
||
|
|
|
||
|
|
Permission is granted to make and distribute verbatim copies of this
|
||
|
|
manual provided the copyright notice and this permission notice are
|
||
|
|
preserved on all copies.
|
||
|
|
|
||
|
|
Permission is granted to copy and distribute modified versions of this
|
||
|
|
manual under the conditions for verbatim copying, provided that the
|
||
|
|
entire resulting derived work is distributed under the terms of a
|
||
|
|
permission notice identical to this one.
|
||
|
|
|
||
|
|
Permission is granted to copy and distribute translations of this manual
|
||
|
|
into another language, under the above conditions for modified versions,
|
||
|
|
except that this permission notice may be stated in a translation
|
||
|
|
approved by the Free Software Foundation. -->
|
||
|
|
<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ -->
|
||
|
|
<head>
|
||
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
|
||
|
|
<title>Multi-dimensional MPI DFTs of Real Data (FFTW 3.3.10)</title>
|
||
|
|
|
||
|
|
<meta name="description" content="Multi-dimensional MPI DFTs of Real Data (FFTW 3.3.10)">
|
||
|
|
<meta name="keywords" content="Multi-dimensional MPI DFTs of Real Data (FFTW 3.3.10)">
|
||
|
|
<meta name="resource-type" content="document">
|
||
|
|
<meta name="distribution" content="global">
|
||
|
|
<meta name="Generator" content="makeinfo">
|
||
|
|
<link href="index.html" rel="start" title="Top">
|
||
|
|
<link href="Concept-Index.html" rel="index" title="Concept Index">
|
||
|
|
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
|
||
|
|
<link href="Distributed_002dmemory-FFTW-with-MPI.html" rel="up" title="Distributed-memory FFTW with MPI">
|
||
|
|
<link href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html" rel="next" title="Other Multi-dimensional Real-data MPI Transforms">
|
||
|
|
<link href="One_002ddimensional-distributions.html" rel="prev" title="One-dimensional distributions">
|
||
|
|
<style type="text/css">
|
||
|
|
<!--
|
||
|
|
a.summary-letter {text-decoration: none}
|
||
|
|
blockquote.indentedblock {margin-right: 0em}
|
||
|
|
div.display {margin-left: 3.2em}
|
||
|
|
div.example {margin-left: 3.2em}
|
||
|
|
div.lisp {margin-left: 3.2em}
|
||
|
|
kbd {font-style: oblique}
|
||
|
|
pre.display {font-family: inherit}
|
||
|
|
pre.format {font-family: inherit}
|
||
|
|
pre.menu-comment {font-family: serif}
|
||
|
|
pre.menu-preformatted {font-family: serif}
|
||
|
|
span.nolinebreak {white-space: nowrap}
|
||
|
|
span.roman {font-family: initial; font-weight: normal}
|
||
|
|
span.sansserif {font-family: sans-serif; font-weight: normal}
|
||
|
|
ul.no-bullet {list-style: none}
|
||
|
|
-->
|
||
|
|
</style>
|
||
|
|
|
||
|
|
|
||
|
|
</head>
|
||
|
|
|
||
|
|
<body lang="en">
|
||
|
|
<span id="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></span><div class="header">
|
||
|
|
<p>
|
||
|
|
Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html" accesskey="u" rel="up">Distributed-memory FFTW with MPI</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
|
||
|
|
</div>
|
||
|
|
<hr>
|
||
|
|
<span id="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></span><h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
|
||
|
|
|
||
|
|
<p>FFTW’s MPI interface also supports multi-dimensional DFTs of real
|
||
|
|
data, similar to the serial r2c and c2r interfaces. (Parallel
|
||
|
|
one-dimensional real-data DFTs are not currently supported; you must
|
||
|
|
use a complex transform and set the imaginary parts of the inputs to
|
||
|
|
zero.)
|
||
|
|
</p>
|
||
|
|
<p>The key points to understand for r2c and c2r MPI transforms (compared
|
||
|
|
to the MPI complex DFTs or the serial r2c/c2r transforms), are:
|
||
|
|
</p>
|
||
|
|
<ul>
|
||
|
|
<li> Just as for serial transforms, r2c/c2r DFTs transform n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
|
||
|
|
real
|
||
|
|
data to/from n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1)
|
||
|
|
complex data: the last dimension of the
|
||
|
|
complex data is cut in half (rounded down), plus one. As for the
|
||
|
|
serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and
|
||
|
|
‘<samp>plan_dft_c2r</samp>’ are the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
|
||
|
|
dimensions of the real data.
|
||
|
|
|
||
|
|
</li><li> <span id="index-padding-4"></span>
|
||
|
|
Although the real data is <em>conceptually</em> n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
|
||
|
|
, it is
|
||
|
|
<em>physically</em> stored as an n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × [2 (n<sub>d-1</sub>/2 + 1)]
|
||
|
|
array, where the last
|
||
|
|
dimension has been <em>padded</em> to make it the same size as the
|
||
|
|
complex output. This is much like the in-place serial r2c/c2r
|
||
|
|
interface (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html">Multi-Dimensional DFTs of Real Data</a>), except that
|
||
|
|
in MPI the padding is required even for out-of-place data. The extra
|
||
|
|
padding numbers are ignored by FFTW (they are <em>not</em> like
|
||
|
|
zero-padding the transform to a larger size); they are only used to
|
||
|
|
determine the data layout.
|
||
|
|
|
||
|
|
</li><li> <span id="index-data-distribution-3"></span>
|
||
|
|
The data distribution in MPI for <em>both</em> the real and complex data
|
||
|
|
is determined by the shape of the <em>complex</em> data. That is, you
|
||
|
|
call the appropriate ‘<samp>local size</samp>’ function for the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1)
|
||
|
|
|
||
|
|
complex data, and then use the <em>same</em> distribution for the real
|
||
|
|
data except that the last complex dimension is replaced by a (padded)
|
||
|
|
real dimension of twice the length.
|
||
|
|
|
||
|
|
</li></ul>
|
||
|
|
|
||
|
|
<p>For example suppose we are performing an out-of-place r2c transform of
|
||
|
|
L × M × N
|
||
|
|
real data [padded to L × M × 2(N/2+1)
|
||
|
|
],
|
||
|
|
resulting in L × M × N/2+1
|
||
|
|
complex data. Similar to the
|
||
|
|
example in <a href="2d-MPI-example.html">2d MPI example</a>, we might do something like:
|
||
|
|
</p>
|
||
|
|
<div class="example">
|
||
|
|
<pre class="example">#include <fftw3-mpi.h>
|
||
|
|
|
||
|
|
int main(int argc, char **argv)
|
||
|
|
{
|
||
|
|
const ptrdiff_t L = ..., M = ..., N = ...;
|
||
|
|
fftw_plan plan;
|
||
|
|
double *rin;
|
||
|
|
fftw_complex *cout;
|
||
|
|
ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
|
||
|
|
|
||
|
|
MPI_Init(&argc, &argv);
|
||
|
|
fftw_mpi_init();
|
||
|
|
|
||
|
|
/* <span class="roman">get local data size and allocate</span> */
|
||
|
|
alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
|
||
|
|
&local_n0, &local_0_start);
|
||
|
|
rin = fftw_alloc_real(2 * alloc_local);
|
||
|
|
cout = fftw_alloc_complex(alloc_local);
|
||
|
|
|
||
|
|
/* <span class="roman">create plan for out-of-place r2c DFT</span> */
|
||
|
|
plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
|
||
|
|
FFTW_MEASURE);
|
||
|
|
|
||
|
|
/* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
|
||
|
|
for (i = 0; i < local_n0; ++i)
|
||
|
|
for (j = 0; j < M; ++j)
|
||
|
|
for (k = 0; k < N; ++k)
|
||
|
|
rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
|
||
|
|
|
||
|
|
/* <span class="roman">compute transforms as many times as desired</span> */
|
||
|
|
fftw_execute(plan);
|
||
|
|
|
||
|
|
fftw_destroy_plan(plan);
|
||
|
|
|
||
|
|
MPI_Finalize();
|
||
|
|
}
|
||
|
|
</pre></div>
|
||
|
|
|
||
|
|
<span id="index-fftw_005falloc_005freal-2"></span>
|
||
|
|
<span id="index-row_002dmajor-5"></span>
|
||
|
|
<p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
|
||
|
|
argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
|
||
|
|
number of <em>complex</em> values to allocate, the number of <em>real</em>
|
||
|
|
values is twice as many. The <code>rin</code> array is then
|
||
|
|
local_n0 × M × 2(N/2+1)
|
||
|
|
in row-major order, so its
|
||
|
|
<code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) +
|
||
|
|
k</code> (see <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>).
|
||
|
|
</p>
|
||
|
|
<span id="index-transpose-1"></span>
|
||
|
|
<span id="index-FFTW_005fTRANSPOSED_005fOUT"></span>
|
||
|
|
<span id="index-FFTW_005fTRANSPOSED_005fIN"></span>
|
||
|
|
<p>As for the complex transforms, improved performance can be obtained by
|
||
|
|
specifying that the output is the transpose of the input or vice versa
|
||
|
|
(see <a href="Transposed-distributions.html">Transposed distributions</a>). In our L × M × N
|
||
|
|
r2c
|
||
|
|
example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
|
||
|
|
the input would be a padded L × M × 2(N/2+1)
|
||
|
|
real array
|
||
|
|
distributed over the <code>L</code> dimension, while the output would be a
|
||
|
|
M × L × N/2+1
|
||
|
|
complex array distributed over the <code>M</code>
|
||
|
|
dimension. To perform the inverse c2r transform with the same data
|
||
|
|
distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
|
||
|
|
</p>
|
||
|
|
<hr>
|
||
|
|
<div class="header">
|
||
|
|
<p>
|
||
|
|
Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html" accesskey="u" rel="up">Distributed-memory FFTW with MPI</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</body>
|
||
|
|
</html>
|